Abstract
The extensive studies on computing by a team of identical mobile robots operating in the plane in Look-Compute-Move cycles have been carried out mainly in the traditional OBLOT model, where the robots are silent (have no communication capabilities) and oblivious (in a cycle, they have no memory previous cycles). To partially overcome the limits of obliviousness and silence while maintaining some of their advantages, the stronger model of luminous robots, LUMI, has been introduced where the robots, otherwise oblivious and silent, carry a visible light that can take a number of different colors; a color can be seen by observing robots, and persists from a cycle to the next. In the study of the computational impact of lights, an immediate concern has been to understand and determine the additional computational strength of LUMI over OBLOT. Within this line of investigation, we examine the problem of forming a sequence of geometric patterns, PatternSequenceFormation. A complete characterization of the sequences of patterns formable from a given starting configuration has been determined in the OBLOT model. In this paper, we study the formation of sequences of patterns in the LUMI model and provide a complete characterization. The characterization is constructive: our universal protocol forms all formable sequences, and it does so asynchronously and without rigidity. This characterization explicitly and clearly identifies the computational strength of LUMI over OBLOT with respect to the PatternSequenceFormation problem.
Highlights
The control and coordination of systems of autonomous mobile robots operating in continuous spaces has been the object of intensive investigations in a variety of fields, including robotics, control, AI, and distributed computing.A
The problem of determining which coreographies can be formed from a given initial configuration, the PATTERNSEQUENCEFORMATION problem, has been studied in the OBLOT model in [9], where a complete characterization was given for the set of the sequences formable from the initial configuration by semi-synchronous robots with rigid movements, assuming chirality
Since traditional robots without lights are the particular case of luminous robots with one color, the results proven in [8] imply that all sequences formable by robots in SSYNC with rigid movements and chirality can be done by asynchronous luminous robots under the same conditions
Summary
The control and coordination of systems of autonomous mobile robots operating in continuous spaces has been the object of intensive investigations in a variety of fields, including robotics, control, AI, and distributed computing. The problem of determining which coreographies can be formed from a given initial configuration, the PATTERNSEQUENCEFORMATION problem, has been studied in the OBLOT model in [9], where a complete characterization was given for the set of the sequences formable from the initial configuration by semi-synchronous robots with rigid movements (i.e., when moving, a robot always reaches its destination), assuming chirality (i.e., clockwise orientation). Theorem 2: A set of n luminous robots starting from initial configuration where all robots are in distinct positions and have the same color, cannot perform a choreography S, if any of the following holds: 1) size(Si) > n, for some Si ∈ S. In the following, we will use size( (t)), q( (t)), and α( (t)) to denote size(L( (t))), q(L( (t))), and α(L( (t))), respectively, and when no ambiguity arises we will omit the variable t
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